The overhead space in an aircraft cabin is conventionally available for storing on-board luggage in box-shaped compartments. Different types of locking mechanisms are used for keeping the luggage boxes or compartments locked, especially during take-off and landing. Different kinds of lids are also known, for example in the form of hinged flaps, slideable doors, or recessible covers made of a plurality of lamellae or parallel slots. Known overhead constructions make it difficult, or at least cumbersome to stow the luggage and to retrieve the luggage, especially for short people.